What Amiibo do in Breath of the Wild!

There's no such thing as "pay to win" in a single player game. People without Amibo's won't get an unfair disadvantage because others use theirs. They can still enjoy the game, but without the rare and exclusive weapons/collectibles. 

So, you are saying its  not pay to win, its Pay 2 Cheat

It's not any more "Pay 2 Cheat" than any other DLC ever released for any game ever, that includes gear or crafting supplies. Is Skyrim's Dawnguard or Dragonborn DLC "Pay 2 Cheat" because you can get gear and spells there that you can't get if you don't have the DLC? How about preorder bonuses from stores that give you an exclusive in game item that boosts a mild stat or has limited uses? The difference here is that the "DLC" is usable across multiple games, and rather than a big increase in content in one game, you get a physical collectible and a bunch of small increases across multiple games. Furthermore, particularly with Nintendo, how does it negatively affect anyone's experience at all for someone to have a little bit of items that some other people might not have? There's not even Trophies/Achievements that could potentially be got easier by players who have Amiibo's, so it doesn't affect anything at all beyond a slightly different personal experience from one player to the next. Which is exactly what DLC in any game ever does.....